CTL, the מסדר קידושיו might be מסעיה לדבר עבירה if he knows that they will do it. I know a rav who was told by a caterer that if he paid cash he would get a discount of $1,000 as the caterer could get away with not declaring it. He asked a dayan and was told that it was not permitted. It may also be illegal to perform a marriage ceremony without a license (here in Israel this is the case). BTW, if one of the parties has not yet received a civil divorce it could cause legal problems for both. I would consult an attorney who specializes in family and benefits law as well as a competent rav first.
Here in Israel common-law marriage (ידועה בציבור) is recognized for purposes such as single-parent family and social insurance purposes – and there are inspectors who check up on people. There once was a law rescinding the pension of IDF widows who remarried but it was repealed because of the hardships it caused. It also did not make much sense as women with high incomes also received it.